Solve 3x^3+x^2-22x+9div3x^2+7x-6

$$3 { x }^{ 3 } + { x }^{ 2 } -22x+9 \div 3 { x }^{ 2 } +7x-6$$

Evaluate

$$3x^{3}+4x^{2}-15x-6$$

Solution Steps

Divide 9 by 3 to get 3.

$$3x^{3}+x^{2}-22x+3x^{2}+7x-6$$

Combine x^{2} and 3x^{2} to get 4x^{2}.

$$3x^{3}+4x^{2}-22x+7x-6$$

Combine -22x and 7x to get -15x.

$$3x^{3}+4x^{2}-15x-6$$

Differentiate w.r.t. x

$$9x^{2}+8x-15$$

Steps Using Derivative Rule for Sum

Divide 9 by 3 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{3}+x^{2}-22x+3x^{2}+7x-6)$$

Combine x^{2} and 3x^{2} to get 4x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{3}+4x^{2}-22x+7x-6)$$

Combine -22x and 7x to get -15x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{3}+4x^{2}-15x-6)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$3\times 3x^{3-1}+2\times 4x^{2-1}-15x^{1-1}$$

Multiply 3 times 3.

$$9x^{3-1}+2\times 4x^{2-1}-15x^{1-1}$$

Subtract 1 from 3.

$$9x^{2}+2\times 4x^{2-1}-15x^{1-1}$$

Multiply 2 times 4.

$$9x^{2}+8x^{2-1}-15x^{1-1}$$

Subtract 1 from 2.

$$9x^{2}+8x^{1}-15x^{1-1}$$

Subtract 1 from 1.

$$9x^{2}+8x^{1}-15x^{0}$$

For any term t, t^{1}=t.

$$9x^{2}+8x-15x^{0}$$

For any term t except 0, t^{0}=1.

$$9x^{2}+8x-15$$